We examine the fairness and intensity of sequential round-robin tournaments with multiple prizes and heterogeneous players. A tournament is called fair if the winning probabilities in each match depend only on the players' characteristics but not on the sequence of matches. We show that tournaments with three players will be fair if and only if the second prize is valued half of the first prize. The optimal prize structure may, however, be subject to a trade-off between fairness and intensity (measured by the players' expected aggregate effort). By contrast, there is no prize structure for which tournaments with more than three players will be fair if the sequence of matches is exogenously fixed. Our analysis suggests that many tournaments of major sporting events are inherently unfair.

我们检查了具有多个奖项和异类玩家的连续循环赛的公平性和强度。如果每场比赛的获胜概率仅取决于球员的特征而不取决于比赛的顺序，则锦标赛称为公平。我们表明，当且仅当二等奖的价值是一等奖的一半时，三名玩家的锦标赛才是公平的。然而，最佳奖品结构可能需要在公平性和强度（由玩家的预期总努力量来衡量）之间进行权衡。相比之下，如果比赛的顺序是外生固定的，那么对于超过三名玩家的锦标赛就不存在公平的奖金结构。我们的分析表明，许多大型体育赛事的比赛本质上是不公平的。